加权残数配点法解正交各向异性板的积分方程

Solution of Integral Equation for Orthotropic Plate by Use of Weighted Residual Collocation Point Method

本文推导了一般各向异性板弯曲的积分方程,运用加权残数配点法求解了正交各向异性板弯曲的积分方程。本文将部分配点取在边界上,另一部分配点取在域外,只用关于挠度的基本积分方程,而不用关于转角的补充积分方程,简化了方程求解和计算程序。由于正交各向异性板没有解析形式的、实用的基本解,本文提出了两种新的近似基本解:加权双三角级数;广义各向同性板解析形式的基本解和加权双三角级数的叠加。算例表明,本文提出的解法和近似基本解适用于各类边界条件的正交各向异性板,具有简单、可靠、精度高等优点。

In this paper, the integral equation for general anisotropic plate is derived. By means of the weighted residual collocation points method the integral equation, for orthotropic plate bending is solved. The method proposed in this paper takes part of collocation points on boundary and others are taken outside plate domain. And it only needs the basic integral equation, about deflection without using complemental integral equation, about rotation. So it simplifies the solution of integral equation. As well as calculation program. It is unable to obtain a practical and analytic fundamental solution. Two new approximate fundamental solutions are proposed in this paper: weight double trigonometric series; The summation of weight double trigonometric series and the analytic fundamental solution for generalized isotropic plate. Examples show that the solving method and approximate fundamental solutions presented in this paper are simple, reliable and quite precise. And they are applicable for various boundary conditions.